Supersonic turbulent fuel-air mixing and evaporation€¦ · Supersonic turbulent fuel-air mixing...

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Supersonic turbulent fuel-airmixing and evaporation

Researchers at the University of Queensland inAustralia claimed on August 16, 2002 a worldfirst - a flight-test of supersonic combustion-an air-breathing supersonic engine, tagged asa scramjet.

An experimental jet broke a worldspeed record on Nov. 17, 2004,cruising at around 7000 mph (M ̴ 10)in a NACA test of cutting edgeScramjet engine technology.

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Plan of presentation

• Objective• The need to understand

fuel-air mixing• Governing equations• Discretization procedure• Solution algorithm• Results• Closing remarks

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The objective of this work is to formulate,implement, and test following the Eulerianapproach, an all speed control volume-basednumerical procedure for predicting turbulent mixingand evaporation of droplets.

Objective

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The need to understand fuel-airmixing

In supersonic combustors, the high flow velocities andshort residence times require that fuel and air mix and burnquickly to avoid excessive long combustors. Therefore,understanding the nature of turbulent mixing and the needfor means to augment the mixing process are essential indesigning more efficient propulsive systems.

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The Ramjet Engine

A ramjet has no moving parts and achieves compression of intake air bythe forward speed of the air vehicle. Air entering the intake of asupersonic aircraft is slowed by aerodynamic diffusion created by theinlet and diffuser to velocities comparable to those in a turbojetaugmenter. The expansion of hot gases after fuel injection andcombustion accelerates the exhaust air to a velocity higher than that atthe inlet and creates positive push.

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The Scramjet Engine

Scramjet is an acronym for Supersonic Combustion Ramjet. Thescramjet differs from the ramjet in that combustion takes place atsupersonic air velocities through the engine. It is mechanically simple,but vastly more complex aerodynamically than a jet engine.

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Governing equations

•Gas Balance Equations

•Droplet Balance Equations

•Turbulence Closure

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Governing equations (cont.)

•Gas Balance Equations

( ) ( )gCg

gt

gt

ggggg ISct

,

,

,.. +

!!

"

#

$$

%

&''='+

(

()

µ*)*) v

( ) ( )gM

D

g

B

ggggggggg Ipt

,.. +++!+!"=!+

#

#FFvvv $%&%&%

( ) ( ) gEg

gt

gt

gggggggg Ihqhht

,

,

,

Pr.. +

!!

"

#

$$

%

&''+()'='+

*

* µ+,+, &v

( ) ( ) ( ) ( )gvapgvapgvapeffYggvapggggvapgg YMYYYt gvap ,,,,,

1..,

!+"#"="+$

$&%&%&% v

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Governing equations (cont.)

•Droplet Balance Equations

( ) ( )dCd

dt

dt

dddddI

Sct,

,

,.. +!

!

"

#

$$

%

&''='+

(

()

µ*)*) v

( ) ( ) dM

D

d

B

ddddddddd Ipt

,.. +++!+!"=!+

#

#FFvvv $%&%&%

( ) ( ) dEg

dt

dt

ddddddd Ihhht

,

,

,

Pr.. +!

!

"

#

$$

%

&''='+

(

( µ)*)* v

( ) ( ) *

2

,

, 8

Pr.. vap

dd

dt

dt

dddddd mD

DDDt

&!

"µ"#"#" $%

%

&

'

((

)

*++=++

,

,v

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Governing equations (cont.)•Turbulence Closure

•Gas Phase

( ) ( ) ( ) dkgkg

k

geff

gggggg SPkkkt

,

,.. +!+""

#

$%%&

'((=(+

)

)*+,

-

µ,+,+, v

( ) ( ) dgkg

T

geff

gggggg Sk

CPk

Ct

,

2

21

,

,.. !!!

!

!"

!#!

$

µ#!"#!"# +%%

&

'(()

*++%

%

&

'

((

)

*,,=,+

-

-v

g

g

ggturb

kC

!"µ µ

2

,=

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Governing equations (cont.)•Turbulence Closure

•Droplet PhaseTo simulate the effect of turbulent spray dispersion, the gas velocity israndomly sampled along the droplet trajectories and the characteristicquantities of the turbulence structure are determined from mean gasflow properties according to:

g

d

g

dg,turbd,turb

k

k

!

!µµ =

22g

d

1

1

k

k

!"+=

687.0d

2

g

d

4/1

x

g32

Re133.01

1D

18

1

L

k1

+=

!!!

"

#

$$$

%

&=

'(

()

))

*

( )( )

g

g

x

kcL

!µ

2/3

4/3

=

Lx and t being the length scale anddissipation time scales of the idealizededdies.

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Discretization procedure

! r(k )"(k)# (k)( )!t

+$. r(k)"(k)u(k)#( k)( ) = $. r (k )% (k)$#(k)( ) + r(k )Q(k )

P

E

S

N

W

Je

Js

Jn

Jw

! +=)(PNB

PNBNBPPbaa""" ""

General Conservation Equation

Algebraic Forms

[ ])k(P

)k( H !=!

[ ] ( )PrP

k

P

kk

P

k

P!"=)()()(

DuHPu)(

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Solution algorithm

The Pressure correction equation:

( ) ( ) ( ) 0rt

rr

k

k)k(

P

)k(

P

Old)k(

P

)k(

P

)k(

P

)k(

P =!"

!#$

!%

!&'

()+*+

(,(- .Su

)(

)(*)()()(*)()( ,,!!

+=+=!+=kkkkkkñññPPP uuu

o

( )[ ]{ }=!"#$k

kkkk

PPrr .SD

)()()*()( oo

%

[ ] !=

"="#)(Pnbf

fP

( ) [ ]!"#

"$%

"&

"'(

)+*+

k

kkk

P

Oldk

P

k

P

k

P

k

PUr

t

rr )*()*()()()()*()(

,-

,, o

o

PCPPPPP

k

P

kk

P

k

P!+=!+=!"#= $$$% **)()()()*( ,, ooo

Duu

! +"=")(PNB

PNBNBPPbPaPa###

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Solution algorithm (cont.)

The sequence of events is as follows:Solve the fluidic momentum equations for velocities.Solve the pressure correction equation based on global mass conservation.Correct velocities, densities, and pressure.Solve the fluidic mass conservation equations for volume fractions.Solve the fluidic scalar equations (k, e, T,Y,D, etc…).Return to the first step and repeat until convergence.

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Results and discussion

Evaporation and Mixing of water droplets injected parallel

to a stream of air:

Subsonic turbulent evaporation and mixing

Supersonic turbulent evaporation and mixing

L

Wd

L= 1 m

W= 0.25 m

d= 0.002 m

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Results and discussion(cont.)

Turbulent evaporation and mixing of water droplets

injected at right angle in a supersonic stream of air

L= 1 m

W= 0.25 m

d= 0.002m

L

d

W

L

d

W

d

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Subsonic turbulent evaporationand mixing

(a)

(b)

(c)

(d)

(e)

Minlet=0.2 Tg=900 K Td=300 K

Fig. 1 (a) Velocity profile, (b) droplet volume fraction, (c) gas temperature, (d) water vapor fraction, and (e) pressure field.

(a)

(b)

(c)

(d)

(e)

Laminar Turbulent

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Subsonic turbulent evaporationand mixing

Fig. 2 Variation of droplet temperature and diameter along the center line of the domain.

0.25 0.5 0.75 1Axial Distance

300

305

310

315

320

325

330

335

340

345

350

7E-05

8E-05

9E-05

0.0001

d dDT

Droplet Temperature

Droplet diameter

M =0.2, k- modelinlet

!

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Supersonic turbulentevaporation and mixing

(a)

(b)

(c)

(d)

(e)

Minlet=2. Tg=900 K Td=300 K


(a)

(b)

(c)

(a)

(b)

(c)

(d)

(e)

Laminar Turbulent

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0 0.25 0.5 0.75 1Axial Distance

300

305

310

315

320

325

330

335

340

9.4E-05

9.5E-05

9.6E-05

9.7E-05

9.8E-05

9.9E-05

0.0001

T dDd

Droplet Temperature

Droplet Diameter

M =2 k- modelinlet

!

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300 400 500 600 700 800 900 1000 1100

Inlet Gas Temperature

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

%Liq

ui d

Mass

Evapora

ted

Fig. 5 (a) The percentage, by mass, of the injected liquid droplets that evaporates at different inlet gas temperatures. (b) The percentage, by mass, of the injected liquid droplets that evaporates at different inlet droplet temperatures.

(b)

(c)

300 310 320 330 340 350 360 370

Inlet Droplet Temperature

3

4

5

6

7

8

9

10

11

12

13

14

15

%Liq

ui d

Mass

Evapor a

ted

(a) (b)

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(b)

(c)

0.5 1 1.5 2

Domain Length

10

12

14

16

18

20

22

%Liq

uid

Mass

Evapora

ted

Fig. 6 The percentage, by mass, of the injected liquid droplets that evaporates for different domain lengths.

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Supersonic turbulent evaporationand mixing with injection at right

angle : case 1

(a)

(b)

(c)

(d)

(e)


(a)

(b)

(c)

(d)

(e)


Laminar Turbulent

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angle : case 1Minlet=2. Tg=900 K Td=300 K

0 0.25 0.5 0.75 1Axial Distance

300

305

310

315

320

325

330

335

340

345

9.3E-05

9.4E-05

9.5E-05

9.6E-05

9.7E-05

9.8E-05

9.9E-05

0.0001

T

dD

d

Droplet Temperature

Droplet Diameter

M =2 k- modelinlet

!


25


angle : case 2

(a)

(b)

(c)

(d)

(e)


(a)

(b)

(c)

(d)

(e)


Laminar Turbulent

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Closing remarks

An Eulerian model for the prediction of variablesize droplet evaporation and mixing at all speedswas presented.The model was tested by solving evaporationand mixing problems in the various Mach numberregimes.Results are promising but still need validationagainst published data.Even though water was used for the droplets, thisis not a model restriction and any other type of fuelcan equally be used.

Supersonic turbulent fuel-air mixing and evaporation€¦ · Supersonic turbulent fuel-air mixing...

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